If you haven't gone to their registration site yet you need to gone ASAP or you won't be able to use it after 10 hours. The serial number is what you enter in to get your activation code from their website. This directly from the CP Forums:

Once you complete your purchase...

Go to: http://www.virtual-fashion.com/html/en/register.php.

Enter your serial number ( Serial Code can be found on your Order Details in you My Stuff section of CP and in the Order Confirmation E-mail sent) and Security Code as displayed on the VF Web Page along with your valid email address.

You will then be directed to a page where you enter a username and password. Once completed you will be given an activation code.
(A confirmation E-mail will be sent to you upon completion).

Once VF has downloaded and been installed, launch VF, go to the VF Resource Manager and enter your activation code, username and password (all of which are case-sensitive).

Your product is now activated.

Note: an Internet connection is required to validate the activation code. If you do not enter the activation code within 10 hours of use, the program will cease to function, so we recommend you do it immediately.